src/math.js

// Copyright 2012 the V8 project authors. All rights reserved.
// Use of this source code is governed by a BSD-style license that can be
// found in the LICENSE file.

"use strict";

// This file relies on the fact that the following declarations have been made
// in runtime.js:
// var $Object = global.Object;

// Keep reference to original values of some global properties.  This
// has the added benefit that the code in this file is isolated from
// changes to these properties.
var $floor = MathFloor;
var $abs = MathAbs;

// Instance class name can only be set on functions. That is the only
// purpose for MathConstructor.
function MathConstructor() {}
var $Math = new MathConstructor();

// -------------------------------------------------------------------

// ECMA 262 - 15.8.2.1
function MathAbs(x) {
  if (%_IsSmi(x)) return x >= 0 ? x : -x;
  x = TO_NUMBER_INLINE(x);
  if (x === 0) return 0;  // To handle -0.
  return x > 0 ? x : -x;
}

// ECMA 262 - 15.8.2.2
function MathAcosJS(x) {
  return %MathAcos(TO_NUMBER_INLINE(x));
}

// ECMA 262 - 15.8.2.3
function MathAsinJS(x) {
  return %MathAsin(TO_NUMBER_INLINE(x));
}

// ECMA 262 - 15.8.2.4
function MathAtanJS(x) {
  return %MathAtan(TO_NUMBER_INLINE(x));
}

// ECMA 262 - 15.8.2.5
// The naming of y and x matches the spec, as does the order in which
// ToNumber (valueOf) is called.
function MathAtan2JS(y, x) {
  return %MathAtan2(TO_NUMBER_INLINE(y), TO_NUMBER_INLINE(x));
}

// ECMA 262 - 15.8.2.6
function MathCeil(x) {
  return -MathFloor(-x);
}

// ECMA 262 - 15.8.2.8
function MathExp(x) {
  return %MathExpRT(TO_NUMBER_INLINE(x));
}

// ECMA 262 - 15.8.2.9
function MathFloor(x) {
  x = TO_NUMBER_INLINE(x);
  // It's more common to call this with a positive number that's out
  // of range than negative numbers; check the upper bound first.
  if (x < 0x80000000 && x > 0) {
    // Numbers in the range [0, 2^31) can be floored by converting
    // them to an unsigned 32-bit value using the shift operator.
    // We avoid doing so for -0, because the result of Math.floor(-0)
    // has to be -0, which wouldn't be the case with the shift.
    return TO_UINT32(x);
  } else {
    return %MathFloorRT(x);
  }
}

// ECMA 262 - 15.8.2.10
function MathLog(x) {
  return %_MathLogRT(TO_NUMBER_INLINE(x));
}

// ECMA 262 - 15.8.2.11
function MathMax(arg1, arg2) {  // length == 2
  var length = %_ArgumentsLength();
  if (length == 2) {
    arg1 = TO_NUMBER_INLINE(arg1);
    arg2 = TO_NUMBER_INLINE(arg2);
    if (arg2 > arg1) return arg2;
    if (arg1 > arg2) return arg1;
    if (arg1 == arg2) {
      // Make sure -0 is considered less than +0.
      return (arg1 === 0 && %_IsMinusZero(arg1)) ? arg2 : arg1;
    }
    // All comparisons failed, one of the arguments must be NaN.
    return NAN;
  }
  var r = -INFINITY;
  for (var i = 0; i < length; i++) {
    var n = %_Arguments(i);
    if (!IS_NUMBER(n)) n = NonNumberToNumber(n);
    // Make sure +0 is considered greater than -0.
    if (NUMBER_IS_NAN(n) || n > r || (r === 0 && n === 0 && %_IsMinusZero(r))) {
      r = n;
    }
  }
  return r;
}

// ECMA 262 - 15.8.2.12
function MathMin(arg1, arg2) {  // length == 2
  var length = %_ArgumentsLength();
  if (length == 2) {
    arg1 = TO_NUMBER_INLINE(arg1);
    arg2 = TO_NUMBER_INLINE(arg2);
    if (arg2 > arg1) return arg1;
    if (arg1 > arg2) return arg2;
    if (arg1 == arg2) {
      // Make sure -0 is considered less than +0.
      return (arg1 === 0 && %_IsMinusZero(arg1)) ? arg1 : arg2;
    }
    // All comparisons failed, one of the arguments must be NaN.
    return NAN;
  }
  var r = INFINITY;
  for (var i = 0; i < length; i++) {
    var n = %_Arguments(i);
    if (!IS_NUMBER(n)) n = NonNumberToNumber(n);
    // Make sure -0 is considered less than +0.
    if (NUMBER_IS_NAN(n) || n < r || (r === 0 && n === 0 && %_IsMinusZero(n))) {
      r = n;
    }
  }
  return r;
}

// ECMA 262 - 15.8.2.13
function MathPow(x, y) {
  return %_MathPow(TO_NUMBER_INLINE(x), TO_NUMBER_INLINE(y));
}

// ECMA 262 - 15.8.2.14
var rngstate;  // Initialized to a Uint32Array during genesis.
function MathRandom() {
  var r0 = (MathImul(18030, rngstate[0] & 0xFFFF) + (rngstate[0] >>> 16)) | 0;
  rngstate[0] = r0;
  var r1 = (MathImul(36969, rngstate[1] & 0xFFFF) + (rngstate[1] >>> 16)) | 0;
  rngstate[1] = r1;
  var x = ((r0 << 16) + (r1 & 0xFFFF)) | 0;
  // Division by 0x100000000 through multiplication by reciprocal.
  return (x < 0 ? (x + 0x100000000) : x) * 2.3283064365386962890625e-10;
}

// ECMA 262 - 15.8.2.15
function MathRound(x) {
  return %RoundNumber(TO_NUMBER_INLINE(x));
}

// ECMA 262 - 15.8.2.17
function MathSqrt(x) {
  return %_MathSqrtRT(TO_NUMBER_INLINE(x));
}

// Non-standard extension.
function MathImul(x, y) {
  return %NumberImul(TO_NUMBER_INLINE(x), TO_NUMBER_INLINE(y));
}

// ES6 draft 09-27-13, section 20.2.2.28.
function MathSign(x) {
  x = TO_NUMBER_INLINE(x);
  if (x > 0) return 1;
  if (x < 0) return -1;
  // -0, 0 or NaN.
  return x;
}

// ES6 draft 09-27-13, section 20.2.2.34.
function MathTrunc(x) {
  x = TO_NUMBER_INLINE(x);
  if (x > 0) return MathFloor(x);
  if (x < 0) return MathCeil(x);
  // -0, 0 or NaN.
  return x;
}

// ES6 draft 09-27-13, section 20.2.2.33.
function MathTanh(x) {
  if (!IS_NUMBER(x)) x = NonNumberToNumber(x);
  // Idempotent for +/-0.
  if (x === 0) return x;
  // Returns +/-1 for +/-Infinity.
  if (!NUMBER_IS_FINITE(x)) return MathSign(x);
  var exp1 = MathExp(x);
  var exp2 = MathExp(-x);
  return (exp1 - exp2) / (exp1 + exp2);
}

// ES6 draft 09-27-13, section 20.2.2.5.
function MathAsinh(x) {
  if (!IS_NUMBER(x)) x = NonNumberToNumber(x);
  // Idempotent for NaN, +/-0 and +/-Infinity.
  if (x === 0 || !NUMBER_IS_FINITE(x)) return x;
  if (x > 0) return MathLog(x + MathSqrt(x * x + 1));
  // This is to prevent numerical errors caused by large negative x.
  return -MathLog(-x + MathSqrt(x * x + 1));
}

// ES6 draft 09-27-13, section 20.2.2.3.
function MathAcosh(x) {
  if (!IS_NUMBER(x)) x = NonNumberToNumber(x);
  if (x < 1) return NAN;
  // Idempotent for NaN and +Infinity.
  if (!NUMBER_IS_FINITE(x)) return x;
  return MathLog(x + MathSqrt(x + 1) * MathSqrt(x - 1));
}

// ES6 draft 09-27-13, section 20.2.2.7.
function MathAtanh(x) {
  if (!IS_NUMBER(x)) x = NonNumberToNumber(x);
  // Idempotent for +/-0.
  if (x === 0) return x;
  // Returns NaN for NaN and +/- Infinity.
  if (!NUMBER_IS_FINITE(x)) return NAN;
  return 0.5 * MathLog((1 + x) / (1 - x));
}

// ES6 draft 09-27-13, section 20.2.2.17.
function MathHypot(x, y) {  // Function length is 2.
  // We may want to introduce fast paths for two arguments and when
  // normalization to avoid overflow is not necessary.  For now, we
  // simply assume the general case.
  var length = %_ArgumentsLength();
  var args = new InternalArray(length);
  var max = 0;
  for (var i = 0; i < length; i++) {
    var n = %_Arguments(i);
    if (!IS_NUMBER(n)) n = NonNumberToNumber(n);
    if (n === INFINITY || n === -INFINITY) return INFINITY;
    n = MathAbs(n);
    if (n > max) max = n;
    args[i] = n;
  }

  // Kahan summation to avoid rounding errors.
  // Normalize the numbers to the largest one to avoid overflow.
  if (max === 0) max = 1;
  var sum = 0;
  var compensation = 0;
  for (var i = 0; i < length; i++) {
    var n = args[i] / max;
    var summand = n * n - compensation;
    var preliminary = sum + summand;
    compensation = (preliminary - sum) - summand;
    sum = preliminary;
  }
  return MathSqrt(sum) * max;
}

// ES6 draft 09-27-13, section 20.2.2.16.
function MathFroundJS(x) {
  return %MathFround(TO_NUMBER_INLINE(x));
}

// ES6 draft 07-18-14, section 20.2.2.11
function MathClz32(x) {
  x = ToUint32(TO_NUMBER_INLINE(x));
  if (x == 0) return 32;
  var result = 0;
  // Binary search.
  if ((x & 0xFFFF0000) === 0) { x <<= 16; result += 16; };
  if ((x & 0xFF000000) === 0) { x <<=  8; result +=  8; };
  if ((x & 0xF0000000) === 0) { x <<=  4; result +=  4; };
  if ((x & 0xC0000000) === 0) { x <<=  2; result +=  2; };
  if ((x & 0x80000000) === 0) { x <<=  1; result +=  1; };
  return result;
}

// ES6 draft 09-27-13, section 20.2.2.9.
// Cube root approximation, refer to: http://metamerist.com/cbrt/cbrt.htm
// Using initial approximation adapted from Kahan's cbrt and 4 iterations
// of Newton's method.
function MathCbrt(x) {
  if (!IS_NUMBER(x)) x = NonNumberToNumber(x);
  if (x == 0 || !NUMBER_IS_FINITE(x)) return x;
  return x >= 0 ? CubeRoot(x) : -CubeRoot(-x);
}

macro NEWTON_ITERATION_CBRT(x, approx)
  (1.0 / 3.0) * (x / (approx * approx) + 2 * approx);
endmacro

function CubeRoot(x) {
  var approx_hi = MathFloor(%_DoubleHi(x) / 3) + 0x2A9F7893;
  var approx = %_ConstructDouble(approx_hi, 0);
  approx = NEWTON_ITERATION_CBRT(x, approx);
  approx = NEWTON_ITERATION_CBRT(x, approx);
  approx = NEWTON_ITERATION_CBRT(x, approx);
  return NEWTON_ITERATION_CBRT(x, approx);
}

// -------------------------------------------------------------------

function SetUpMath() {
  %CheckIsBootstrapping();

  %InternalSetPrototype($Math, $Object.prototype);
  %AddNamedProperty(global, "Math", $Math, DONT_ENUM);
  %FunctionSetInstanceClassName(MathConstructor, 'Math');

  %AddNamedProperty($Math, symbolToStringTag, "Math", READ_ONLY | DONT_ENUM);

  // Set up math constants.
  InstallConstants($Math, $Array(
    // ECMA-262, section 15.8.1.1.
    "E", 2.7182818284590452354,
    // ECMA-262, section 15.8.1.2.
    "LN10", 2.302585092994046,
    // ECMA-262, section 15.8.1.3.
    "LN2", 0.6931471805599453,
    // ECMA-262, section 15.8.1.4.
    "LOG2E", 1.4426950408889634,
    "LOG10E", 0.4342944819032518,
    "PI", 3.1415926535897932,
    "SQRT1_2", 0.7071067811865476,
    "SQRT2", 1.4142135623730951
  ));

  // Set up non-enumerable functions of the Math object and
  // set their names.
  InstallFunctions($Math, DONT_ENUM, $Array(
    "random", MathRandom,
    "abs", MathAbs,
    "acos", MathAcosJS,
    "asin", MathAsinJS,
    "atan", MathAtanJS,
    "ceil", MathCeil,
    "cos", MathCos,       // implemented by third_party/fdlibm
    "exp", MathExp,
    "floor", MathFloor,
    "log", MathLog,
    "round", MathRound,
    "sin", MathSin,       // implemented by third_party/fdlibm
    "sqrt", MathSqrt,
    "tan", MathTan,       // implemented by third_party/fdlibm
    "atan2", MathAtan2JS,
    "pow", MathPow,
    "max", MathMax,
    "min", MathMin,
    "imul", MathImul,
    "sign", MathSign,
    "trunc", MathTrunc,
    "sinh", MathSinh,     // implemented by third_party/fdlibm
    "cosh", MathCosh,     // implemented by third_party/fdlibm
    "tanh", MathTanh,
    "asinh", MathAsinh,
    "acosh", MathAcosh,
    "atanh", MathAtanh,
    "log10", MathLog10,   // implemented by third_party/fdlibm
    "log2", MathLog2,     // implemented by third_party/fdlibm
    "hypot", MathHypot,
    "fround", MathFroundJS,
    "clz32", MathClz32,
    "cbrt", MathCbrt,
    "log1p", MathLog1p,   // implemented by third_party/fdlibm
    "expm1", MathExpm1    // implemented by third_party/fdlibm
  ));

  %SetInlineBuiltinFlag(MathCeil);
  %SetInlineBuiltinFlag(MathRandom);
  %SetInlineBuiltinFlag(MathSin);
  %SetInlineBuiltinFlag(MathCos);
}

SetUpMath();